On averaging methods for partial differential equations

Abstract

The analysis of weakly nonlinear partial differential equations both qualitatively and quantitatively is emerging as an exciting eld of investigation In this report we consider specic results related to averaging but we do not aim at completeness The sections and contain important material which is not easily accessible in the literature Of the literature which we will not discuss in detail we should mention Formal approximation methods which have been nicely presented by Cole and Kevorkian A number of formal methods for nonlinear hyperbolic equations on unbounded domains have been analysed with respect to the question of asymptotic validity by van der Burgh